A does half as much work as B = $\dfrac{1}{2}$ B of work in three-fourths of the time
∴ A does $\dfrac{1}{2}$B / $\dfrac{3}{4}$T = $\dfrac{2}3{B}$ of work in t time.
Therefore, work done by A = $\dfrac{2}3{B}$
Together they take 18 days to complete a work,
in 18 days they have done 1 job
in 1 day they have done $\dfrac{1}{18}$ job
A + B = $\dfrac{1}{18}$
or, $\dfrac{2}3{B}$ + B = $\dfrac{1}{18}$
or, $\dfrac{5}3{B}$ = $\dfrac{1}{18}$
or, B = $\dfrac{3}{5*18}$
or, B = $\dfrac{1}{30}$ job/day
so,if B completes $\dfrac{1}{30}$ of a job in a day,then B takes 30 days to complete the job.
Therefore, A = $\dfrac{2}3{B}$
= $\dfrac{2}{3}$ * $\dfrac{1}{30}$
= $\dfrac{2}{3*30}$
= $\dfrac{1}{45}$ job/day
so,if A completes $\dfrac{1}{45}$ of a job in a day,then A takes 45 days to complete the job.